Transport of Sand Mixtures Including Consideration of Field Data, Threshold of Motion, Fai1 Velocity and Bed, Suspendedand Total Load Transport

fttOranlicsResearctt Wa[ingford

TRANSPORTOF SANDMIXTURES A LITERATUREREVIEW

April 1989 Report SR 200

Registered Office: Hydraulics Research Limited, Wallingford, Oxfordshire OXl0 8BA. Telephone: O49l 35381. Telex: 848552 This report describes work funded by the Department of the Environment under Research Contract PECD7/6/II2 for which the DoE nominated officer was Dr R P Thorogood. It is published on behalf of the Department of the Environment but any opinions expressed in this report are not necessarily those of the funding Department. The work was carried out by Dr N Walmsley and Dr G V Miles in the Tidal Engineering Department of Hydraulics Research, Wallingford, under the managementof Mr M F C Thorn.

@Cro*n copyright 1989 Published by permission of the Controller of Her Majesty's Stationery Office ABSTRACT

The study of sediment transport generally is very difficult but more so in the case of estuaries because:

- the water movementsare continually changing with the rise and faII of the tide

- certain sediments are not found in someparts, leading to unsaturated loads in the water

- a wide range of sediment exist,s on the bed and in suspension.

In recent years sediment transport models have been developed and used for rnaking engineering assessments of the impact of works on the sediment regime. At present the fulI potential of the models cannot be realised becauseof the lack of calibration and verification data, and gaps in our understanding of the fundamental sedimentation processes.

Recent research, funded by the Department of the Environment under Research Contract PECD7/6/56, demonstratedthat computermodels of sediment transport can simulate the effects of variable tidal movementsand partly saturated loads of sediment. The objeetive of the present research project is to consider the problems associated with mixtures of sediment.

The first phase of this project included a literature review of the transport of sand mixtures including consideration of field data, threshold of motion, faI1 velocity and bed, suspendedand total load transport. This report summarisesthe main references on the subject and contains a brief description of the latest theories being considered by other workers in this field. The main factors which will need to be taken into account in the computer model of sediment mixtures have been identified as the incorporation of different saturation concentrations for different mixtures of size fractions, different bed exchangerates resulting from different settling velocities and armouring of the bed by coarser grains, and variable bed composition arising from differential settling and resuspension.

The information obtained from the literature review will be assessedin the next stage of the work and used to formulate a computer model for simulating the transport of mixtures. This will be described in the main contract report due in the Spring of 1990.

CONTENTS

Page

1 INTRODUCTION 1

2 GENERALBACKGROUND 2

2,I Mixture theory z a 2.2 Field and flume studies z 2.3 Numerical models 4

TRANSPORTOF SANDMIXTURES 5

3. I Threshold of sediment motion 5 3.2 Fa11 velocity 7 3.3 Bed load transport X 3.4 Suspendedload transport 10 3. 5 Total l-oad transoort L2

4 DISCUSSION T2

5 ACIO{OWLEDGEMENTS 13

6 REFERENCES I4

APPENDICES

Appendix I - Main workers in the field Appendix II - Additional references

1 INTRODUCTION The numerical" model prediction of sediment transport plays an import.ant role in assessing the impact of engineering works in tidal est,uaries. The models can be used to assess deposition,/erosion problems during the early design stages and can identify possible future maintenance commitmenLs such as the dredging of shipping channels.

A lot of work has been done in the past on the motion of uniform sands in one dimensional f1ows. In tidal estuaries the problems become more difficult because the water movements are continually changing with the rise and fall of the tide, a wide range of sediment exi-sts on the bed and in suspension and certain sediments are found in some parts but not in others which may lead to unsaturated loads in the water co]umn.

Tn order to irnprove the usefulness of existing sediment transport models in engi-neering applications a number of developments have been outlined in relation to the modelling sand mixtures:

- incorporation of different saturation concent.rations for different size fractions

- different bed exchange rates resulting from variable settling veLocities

- variable bed composition arising from differential erosion and deposition

- the possibility of armouring of finer grains by coarser grains

- efficient and accurate methods of calculating saturation concentrations - ini-tialisation of bed composition in situations of variable supply of erodible material

The aim of this l-iterature review was to identifv the key workers in this field of study and to bring together many of the relevant references. This interim report is not an in depth technical review but is intended as a reference guide for the researchers undertaking the next phase of the research contract.

GENERAL BACKGROUND

2.L Mixture theory The transport of fine material-s in turbulent fluid flow plays an important role in a broad range of disciplines and this has been refLected in the research literature. Fluid-solid mixture theory has been developed (McTigue, 1981) which models both the fluid and particulate phases as continua whilst taking account of turbulent fluctuations of the velocities and concentrations. Constitutive equations describing the shear stresses occurring in a mixture have been derived by Ackermann and Shen Q982) [see also Shen and Ackermann ( 1982) I whil-st other researchers have investigated bouyancy forces and concentration distributions in fluid-soIid mixtures (Zhaoyin, L987, and Zhaohui and Ti-ancheng, I9B7).

2.2 FieId and flume studi-es One of the drawbacks of modelling transport of sand mixtures in estuaries is the dearth of field data. However, in recent years a number of in-situ sedimentation studies have been undertaken by Vale and Sundby (1987), Jarvis and Riley (1987), Bedford et aI (1987) which reflect an increasing concern in the lack of relevant field data for the assessment of transport formul-ae and rnathematical model-s. One of the most extensive sedimentation surveys to be reported i-n the literature was carried out by Allen (1971) in the Gironde estuary. He monitored tidal current and lrave induced transport and investigated their effect on the grain size distributions in the estuary. This data was later used by Owens (1986) as validation data for his sediment transport model.

The pattern of naturally occurring grain size distributions is often approximated by a Gaussian or normal- distribution where the 1og histogran approximates to a parabola. Bagnold and Barndorff-Nielsen (1980), however, found that measured sand grain distributions often approxi-mate to a hyperbolic distrj-bution. Their findings were further substantiated by Deigaard and Fredsoe ( 1978) who showed, by simulation, that originally log-norrnally distributed sand will tend to become J-og-hyperbolically distributed after sorting. Work on size distri-butions of sand has been eontinued by Barndorff-Nielsen and Christiansen (1988) whose field studies have shown that the mass-size distributions of sands vil1 vary depending on whether they are from a predominantly depositional environmental- or predominantly erosional environment.

The development of numerical- models to simulate graded sediments has demanded that there be complementary physical model studies in order to gain a full understanding of the physical processes encountered in graded sediments (White, I972; Bridge, 1981; Westrich and Juraschek, 1985; Ribberink, 1987). In particular, Allard (1987) has carried out a series of well controlled flume experiments using sand particles in an effort to isolate certain phenomenaand to assess their relative importance. More recently, Wilcock and Southard ( 19BB) undertook a large range of flume studies on a range of graded sediment samples to investigate incipient motion of the individual grain sizes. Rakoczi (1987) has aLso investigated the effect of sediment mixtures on initiation and development of sediment motion in a series of Iaboratory investigations .

2.3 Numerical models The majority of sediment transport research, whether it be flume experiments, field studies or numerical model development, has been carried out for steady uniform flow conditions. Efforts have been made to develop more advanced models to handle unsteady and non-uniform conditions (Brownlie, 1981; Krishnappen, 1981; Tsujinoto, 1987 and Lyn, 1987) but these are generally only applicable to sediment transport in river channels. However, Markofsky et aI (1985) have developed a model specifically for use in tidal waters. Using their model, they investigated the sensitivity of model results to numerical as wel-l as physical parameters such as discharge, l-ocation of sediment source, stratification and tidal motion. In particular, they investigated methods of limiting the numerical- diffusion generated within the model.

In recent years a number of one dimensi-on models have been developed to take account of graded sediments (Borah et aI, I9B2; Karim and Kennedy, 1985; Karim and Ho11y, 1986) which show good correlations with flume experiments but which falter vhen compared with field dat,a. Lu and Shen (1985) chose Lo investigate the use of an existing sediment transport formula, i.e Einstein's, and found that Einstein's hiding factor could in fact provide reasonable bed load esLimales.

Ce1ik and Rodi (1985) proposed a model which involved new approaches for determining eddy-diffusivity, transport capacity and bed-boundary conditions. The model was applied to non-equilibrium transport situations and close agreement between prediction and measurement was found. An afternative two-dimensional vertical model was proposed by van Rijn (1986) in which finite-element methods lrere used to solve the convecti-on-diffusion equation. The model developed by Lee and Ahn (1986) r.rasderived from convective-diffusion theory but they included a hindered settling effect of the particles and the vertical veloci-ty component due to tidal movement. A series of model tests reveafed the sensitivity of sediment transport to these parameters and demonstrated a hysteresis effect of the sediment concentration between flood and ebb tides. Temporal lag between variations in tidal flow and corresponding variat.ions in sediment concentrations were also evident, parLicul-arly for grain sizes r"rith low fall velocities.

TRANSPORTOF SANDMIXTURES

J..t Threshold of sediment motion The importance of the bed shear stress as the governi-ng mechanism causing sediment motion has been recognised for many years and initiation of motion is generally expressed in terms of applied bed shear stress in the form of a Shields' curve (Shields, 1936). Miller et aI 0977) have used carefully selected data for the initiation of motion under unidirectional fl-ow conditions to develop a nodified Shields-type threshold diagram to extend the limits of the original diagram by three orders of magnitude. However, one of the limitations of the empirical relationships they derived were the grain size distributions used in the experiments. These were fai-rly cLosely graded whereas it is known that naturally occurring sediments generally have a much wider size distribution. Other researchers have developed Shields-type threshofd curves for graded material. fn particular, Singhal et aI (1980) conducted a series of experiments using naturally occurring sands. They found that rather than following Shields' curve the experimental data gave aLternative relationships for each size of bed material- thereby indicating that there was an interaction due to the grading of the sand. They further found that the data could be grouped corresponding to different values of turbulence coefficient which suggested that Shields curve was derived in the short turbulence coefficient range.

Hammondet al ( 1984) undertook a number of in-si-tu studies in tidal areas where the bed material was classified as a gravel (2 - 50mm). Comparisons betlreen observed data, Shields' curve and their own flume experiments were conducted. As expected with graded bed material-, they found that the larger grains experienced a disproportionately large fraction of the bed shear stress due to their increased exposure and this resulted in their threshold of motion being lower than that predicted for a uniform bed. These experiments helped to reinforce the importance of grain protrusion in coarsely packed, non-cohesive grains. r+ ':^ 11-- r L rD Ssrrer 4I ay assumedthat the tractive force ar. initi-alisation of motion will be the same as that at which the motion ceases. Reid and Frostick ( 1984) have shown that this is not necessarily the case when considering coarse-grained mixtures. Their field studi-es on coarse-grained alluvial streams indicated a hysteresis effect in which the threshold of motion was initiated at one value of the shear stress but that motion rras ceased at a much lower shear stress than that predicted by the Shields curve. Whilst this may not be directly applicable to sand transporL, it does indicate a need to consider possible hysteresis tSpe effects in bed load transport. The threshold of motion cannot be considered as a purely det.erministic phenomenonbecause of the fluctuations of bottom flow and Lhe randomness of both particle size and their position in the bed. The random variable approach was adopted by many of the earlier researchers, such as Einstein (1942), and more recently improved stochastic models have been developed (Mingmin and Qiwei, 1982) which incorporate a combined method of mechanistics and probability.

3.2 Fa1I velocity Sediment transport calculations and mathematical modelling of erosion and deposition generally require an estimate of the sediment settling, or fa1l, velocity. Because the caLcul-ations are sensitive to faII velocity best estimates are essential. In the 1970's Zanke (1977) derived an expression for sand particles (0.1 - 1.Omm),and for coarser particles van Ri-jn (1984) gives an alternative expression. Of particular use in sand transport calculations, Hallermeier (1981) utilised published measurements of faII velocities of commonly occurring sand particles to develop an empirical relationship for use with fine, medium and coarse sands.

Refinements of fall velocity calculations to take account of shape factors (Prashun and Knofczynski, 1985) and concentration dependent falI velocities (Lavelle and Thacker, i97B) have been proposed in recent years. However, a limiting fact.or in fall velocity data lies j-n the fact that the majority of tests are carried out under controlled laboratory conditions. Efforts are now being made to carry out in-situ fall velocity measurements (van Rijn and Nienhuis, 1985) and the effect of uniform flow on particle settl-ement has also been considered (Li and Shen, 1975). Bed load transport Sediment mixtures introduce an additional degree of complexity into bed load transport calculations. In the past, a number of bed load transport formulae have been developed vhich are based on an effective, or representative, grain size. For use with sediment mixtures the fundamental approach has been (instead of adopting a single representative sediment size) to split the sediment up in to a number of size ranges and to take a representative sediment diameter for each range. Size distribution and particle interaction, however, are knor,m to play an important rol-e in transport processes and attention is now being focussed in this area. The physical- processes to be considered are, on the one hand, a sheJ-tering of finer grains by larger grains thereby reducing their transport rate; on the other hand, larger grains are more exposed than they vould otherwise be in a uniform bed and their transport is greater due to the larger fluid forces they experience

Proffit and Sutherl-and (1983) modified exist,ing bed load formulae for use with non-uniform sediments by defining an exposure correction factor which al1ows for the increased mobility of coarse particles and reduced mobility of finer particles, as compared with their mobility in a uniform sediment bed. Acceptable correlation with laboratory controlled data was found by Profitt and Sutherland but, as is often the case, comparison with field data was less successful. The variation between bed material distribution to transported material distribution was thought to be the prime reason for the discrepancies. Systematic tests to isolate the effect of bed material gradation and sorting on bed load transport are relatively scarce but their importance was i-nvestigated by Klaassen (1987). He found that verticaL sorting of bed material had an appreciable effect on bed form dimensions and hence resistance to flow and transport rates. Klaassen et al- (1987) have furthered their work in the dune regime area and found, contrary to the flat bed case, that the transport rates of coarser grains is reduced. The reduction in transport rate was due to a temporary storage of coarse grains in the troughs of adjacent dunes.

Misri et aI (1984) undertook an extensive experimental program to investigate the bed load transport of non-uniform sediments and made comparisons with predictions using Einstein's method (Einstein, 1942). The predicted transport varied considerably from these experimental results and Misri et al evolved an alternative method of calcul-ating transport rates in non-uniform mixtures. They developed a coefficient sinilar to Einstein's sheltering coefficient which took account of the sheltering of finer grains but also increased the exposure of coarser grains. Their work was found to give satisfactory results for Laboratory data but the method did not give good results when compared with field data. Samagaet al ( 1986) recognised some of the inadequacies of Proffit and Sutherland's and Misri et aI's experimental studies and undertook a further set of flume studies for non-uniform sediments. The studies confirmed Misri et al-'s findings concerning the inadequacies of Einstein's method and due to the much wider range of variables studied led to an improved exposure correction factor. This had the advantage of being based on a combination of flume and field data.

An important feature of sediment transport in tidal estuaries are spatial and temporal lag effects. These can be defined as the alluvial system's inability to irunediately overcome constrained sediment boundary conditions and to immediately respond to an imposed change in discharge. A one dimensional unsteady flow and sediment routing model with the ability to incorporate these effects is described in Phillips and Sutherland (1985). The performance of the model was test.ed against laboratory flume experiments and a good correl-at.ion between simulated and measured sediment hydrographs and yields were reported. This was a continuation of Sutherland's previous research in this fiel-d which included investigation of non-equilibriurn bed load transport in steady flows (BeII and Sutherland, 1983) and his work vith Proffit (Proffit and Sutherland, 1983) on non-uniform sediments.

In recent years Armanini and di Silvio (1987) developed a model- to simulate erosion/depositi-on in tidal channels with non-uniform bed material. They recognised the shortcomings of using local and instantaneous equilibrium conditj-ons. The phase shift between hydrodynamic and sedi-mentologic quantities was incorporated in their model by the inclusion of spatial and temporal lag effects. In their study of the evol-ution of a trench dredged across a tidal channel, they found the results were less sensitive to the composition of the sediment mixture than in similar studies using steady flow (Armanini and di Silvio, 1985).

3.4 Suspended load

+e^----^-+ L! Arr-PUt L The suspended transport of uniform sediment.s has been studied extensi-vely during the last five decades. Suspended load transport describes the motion of particles which are fully surrounded by the fluid. Owing to the weight of the particles there is a tendency to settl-e but this is counter balanced by the irregular, turbulent velocity componentsof the fluid. The hydraulic conditions of the fluid determine whether a particular grain fraction is in suspension or nol. There exists an interchange between the bed load and suspended load in addition to that between the bed l-oad and the bed.

10 During suspended load transport there is a tendency for the grain fractions to undergo size-sorting (Sengupta 1975). The grain size distribution at different heights above the bed becomes skewed when compared with that of the bed load material. The resulting suspended load distribution has been found to be a function of the initial bed load di-stribution and the flow velocity (Sengupta, 7979).

Samagaand Ranga Raju (1985) carried out a series of fl-ume experiment.s and field tests to gain a better understanding of the physical processes affecting suspended transport of mixtures. The processes involved are : the sheltering or exposure effect which influences the concentration of size fractions close to the bed; the interference of one size fraction with the others in the process of entrainment and suspended load, thereby affecting the exponent in the sediment distribution equation. The findings of Samagaand Ranga Raju concluded that some of the well established suspended sediment transport methods gave poor results for the individual size fractions in a mixture. An alternatj-ve method was developed, based on a correction factor for each size fraction, rrhich gave better results although only one set of field data was used in the comparison. Further validation is required to fulIy verify the method.

Samagaet al's interest in this field of research has included investigations into the concentration distributions of sediment mixtures (Samagaet aI, 1986). The agreement between existing predictors and field data was found to be unsatisfactory. The field data suggested that the sediment distribution exponent for any size fraction in a mixture was not constant over the whole depth of flow. A two layer model was proposed which gave improved results against limited field data.

l1 3.5 Total load transport The total bed material load is the sum of the bed load and suspended load but excLudes the wash 1oad. The present day methods for the calculation of total load are of two kinds. Firstly, a sutnmation of the bed load and suspended load and, secondly, methods which directly relate total load with the flow parameters. In the case of non-uniform sediments the transport rate of one size fraction is strongly affected by the presence of the other fractions and calculations based on a representative size fraction wi]l noL be correct.

Ackers and White's sediment transport method was modified by Day ( 1980) for use with graded sediment by including an initial motion parameter for each size fraction.

Samagaet al (1985) proposed a rnethod for the computation of total load transport of each size fraction in the bed material. The method used the transport reLationships of uniform bed material as a basis but then introduced a sheltering coefficient to account for the graded bed material. The resulting semi-empirical total load transport formula was based on flurne data but verification of the method with field data was not reported. A full- assessment of the method has therefore yet to be made.

DISCUSSION This interim report has highlighted the key workers researching into the transport of sand mixtures and has identified the presently available relevant literature. This report does not contain an in depth technical assessment of the literature but merely indicat.es what ideas and information are available for the use in next phase of the research project.

T2 The published research highlights the need to model interactions between size fractions rather than attempting to seem the effect of quasi-independent fracLions. Although suitable studies are not numerous, models should be validated against field data wherever possible as comparisons with laboratory measurements often give falsel-y optimistic results

5 ACKNOWLEDGEMENTS I t+rou1dlike to thank R Bettess, R L Soulsby, E Atkinson, P Lawrence, I Meadowcroft, N V M Odd, B R Wild and G V Miles for their assistance in carrying out this study.

t3 6 REFERENCES Ackermann N L and Shen H (1982). Stresses in rapidly sheared fluid - solid mixtures. ASCEJ of Engineering Mech Div, vo1 198, No EM1, pp95-113.

Allard J (1987). Sediment transport in rivers - research activities of the National Hydraulics Laboratory (France). Euromech215, Genova, Italy, pp133-136.

Allen G P (1971). Relationship beLweengrain size distribution and current patterns in the Gironde estuary (France). J of Sedimentary Petrology, vol 41 No l, pp74-BB.

Armanini A and di Sil-vio (1985). Transport of suspended sediments along channels with a trench. XXI Congress of IAHR, vo1 3, Melbourne, Australi-a.

Armanini A and di Silvio c (1987). Erosion - deposition processes in tidal channels with non-uniform bottom material. Congress of IAHR, Lausanne, Switzerland.

Bagnold R A and Barndorff-Nielsen O (1980). The pattern of natural size distributions. Sedimentology, vol 27, pp1l9-207.

Barndorff-Nielsen O E and Christiansen C (1988). Erosion, deposition and size distributions of sand. Proc. of R. Soc. vol 4I7, pp335-352.

Bedford K W, Wai O, Libicki C M and von Evra R (1987). Sediment entrainment and deposition measurements in Long Island sound. ASCEJ of Hydraulics Engineering, vol 113, No 10, pp1325-1342.

T4 BeIl R G and Sutherland A J (1983). Non equilibrium bedload transport by steady f lor"rs. ASCEJ of Hydraulic Engineering, vol 109, No 3, pp357-367.

Borah D K, Alonso C V and Prasad S N (i982). Routing graded sediments in streams : applications. ASCEJ of Hydraulic Engineering, vol 108, no HYI2, pp1504-1517.

Bridge J S (i981). Hydraulic interpretati-on of grain - size distributions using a physical model for bedload transport. J of Sedinentary Petrology, vol 51 No 4, ppl109-1124.

Brownlie W R (1981). Unsteady sediment transport modelling. Proc of Speciality Conf. Water forum '81, San Fransisco, USA, pp1193-1200.

Celik I and Rodi W (1985). Mathematical modelling of suspended sediment transport in open channel-s. 2lst IAHR Congress, Melbourne, Australia, pp533-538.

Day T J (1980). A study of the transport of graded sediments. Hydraulics Research Station Report No IT 190, pp10.

Deigaard R and Fredsoe J (1978). Longitudinal grain sorting by current in alluvial streams. Nordic Hydral., vo1 9, pp7-16

Einstein H A ( 1942). Forrnulas for the transportation of bed-load. Trans. ASCE,vol 107.

Hallermeier R J (l9Bl). Terminal settling velocity of commonly occurring sand grains. Sedimentology vo1 28 pp859-865.

l5 HammondF D C, Heathershaw A D and Langhorne D N ( 1984) . A comparison between Shields threshold criterion and the movement of loosefy packed gravel in a tidal channel. SedimentoJ-ogyvol 31, pp5I-62.

Jarvis J and Riley C (1987). Sediment transport in the mouth of the Eden estuary. Estuarine, coastal and shelf science, vol 24, pp463-481.

Karim M F and Ho11y F M (1986). Armouring and sorting simulation in a1luvial rivers. ASCEJ of Hydraulic Engineering, vol 112, No B, pp705-715.

Karin M F and Kennedy J F (1985). Kinematic analysis of bed degradation in alluvial streams wit,h non-uniform sediment. 21st IAHR Congress, Melbourne, Australia, pp554-560.

Klaassen G J (1987). Experiments on the effect of gradat,ion on sediment transport phenomena. Euromech 215, Genova, Italy pp235-24l.

Kl-aassenG J Ribberink J S and de Ruiter J C C (1987). On the transport. of mixtures in the dune phase. Euromech215, Genova, Ita1y, pp2I2-2I6.

Krishnappen B G (1981). Field verification of an unsteady non-uniform sediment laden flow modeI. 19th IAHRCongress, NewDelhi, India, pp2|7-229.

Lavelle J W and Thacker W C (1978). Effects of hindered settling on sediment concentration profiles. IAHR Jnl of Hydraulic Research, vol 16, No 4 pp347-355.

Lee J K and Ahn S H (1986). Model of diffusi_on movement of suspended load due to tida] f1ow. 5th IAHR Congress, Asian and Pacific Regional Division, Seoul, Republic of Korea, ppI29-L42. Li and R M and Shen H W (1975). Solid particle settlement in open-channel flow. ASCEJ of Hydraulie Engineering, vo1 101, No HY7, pp917-93I.

Lu J Y and Shen H W (i985). Evaluation of H A Einstein's hi-ding factor for transport of non-uniform sediment sizes. 2lst IAHR Congress, Melbourne, Australia, pp561-564.

Lyn D A (1987). Unsteady sediment transport modelling. ASCEJ of Hydraulic Engineering, vol 113, No 1, pp1-5.

McTigue D F (1981). Mixture theory for suspended sediment transport. ASCEJ of Hydraulic Engineering, vol 107, No 6, pp659-673.

Markofsky M, Lang G and Schubert R (1985). Suspended sediment transport in tidal vraters: turbidity maximum, numerical sinulation, physical aspects. 21st IAHR Congress, Melbourne, AusLralia, pp130-I37 .

Mill-er M C, McCave I N and Kornar P D 0977). Threshold of sediment motion under unidirectional currents. Sedimentology, voJ- 24, pp5o7-527.

Mingmin H and Qiwei H (1982). Stochastic model of incipient sediment motion. ASCEJ of Hydraulics, vol 108, No HY2, pp2II-224.

Misri R L, Garde R J and Ranga Raju K G (1984). Bedload transport of coarse non uniform sediment. ASCEJ of Hydraulic Engineering, vo1 110 No 3, pp312-328.

Owens P H ( f986) . Mathematical modelling of sediment transport in estuaries. PhD thesis, Univ. of Birmingham, UK 22Opp.

1.7 Phi-11ips B C and Sutherland A J (1985). Numerical- modeJ-ling of spatial and temporal 1ag effects in bed load sediment transport. 21st IAHR Congress, Melbourne, Australia, pp571-576.

Prashun A L and Knofczynski M (1985). Improved computation of faI1 velocity. 2lst IAHR Congress, Melbourne, Australia, pp 349-354.

Proffitt G T and Sutherland A J (1983). Transport of non-uniform sediments. IAHR J of Hydraulic Research vol 21 No 1, pp33-43.

Rakoczi L (1987). Effect of granulometry on sediment motion : a new approach. IAHR Congress, Lausanne, Switzerland, pp154-159.

Reid I and Frostick L E (1984). Particle interaction and its effect on the threshold of initial and final bedload motion in coarse alluvial channels. Sedimentology of gravels and conglomerates, Canadian Society of Petroleum GeoLogists, Memoir 10, pp61-68.

Ribberink J S (1987). Bed-load transport of non-uniform sedimenL: physical phenomena and morphological- modelling. Euromech215, Genova, ftaly pp208-21 1 . van Rijn (1984). Sedimenttransport, Part IIf: Bedforms and all-uvial roughness. ASCEJ of Hydraulic Engineering, vo1 110, No 11, pp1613-1641. van Rijn (1986). Mathematical modelling of suspended sediment in non uniform fl-ows. ASCEJ of Hydraulic Engineering, vo1 112, No 6, pp433-455. van Rijn L C and Nienhuis L E A (1985). In-situ determination of fall velocity of suspended sediment. 21st IAHR Congress, Melbourne, Australia, 1985 pp145- 148 . 1B SamagaB R, Garde R J and Ranga Raju K G (1985). Tota1 l-oad transport of sediment mixtures. Irrigation and Power Journal, vol 42, No 4, pp345-353.

SamagaB R, Ranga Raju K G and Garde R J (1986). Suspended load transport of sedj-ment mixtures. ASCEJ of Hydraulics Engineering, vo1 112, No 11, ppi019-1035.

SamagaB R and Ranga Raju K G (1985). Concentration distribution of sediment mixtures in open-channel flow. IAHR J of Hydraulics Research, vol 23, No 5, pp467-483.

SamagaB R, Ranga Raju K G and Garde R J (1986). Bed load transport of sediment mixtures. ASCEJ of Hydraulics Engineering, vol 112, No 11, pp1003-1018.

Sengupta S (1975). Size-sorting during suspension transport - lognormality and other characteristics. Sedimentology, vol 22, pp257-273.

Sengupta S (1979). Grain size distribution of suspended load in relation to bed materials and flov velocity. Sedimentology, vol 26, pp63-82.

Shen H and Ackermann N L (1982). Constitutive relationships for fluid-solid mixtures. ASCEJ of Engineering Mech Div, vo1 108, No EM5, pp 748-763.

Shields A (1936). Awendungder Ahnl-ichkeitsmechanik and Turbulenzforschung auf die Geschiebebe - bewegung, Mitteil. Preuss. Versuchsanst. Wasser, Erd. Schiffshau, Berlin, No 26.

Singhal M K, Mohan J and Agarwal-A K (1980). Crit.ical tractive force for cohesionless graded material. Irrigation and Power Journal, vol 37, No 2, pp 2r9-224.

19 Tsujimoto T (1987). Non-uniform bed load transport and equilibrium bed profile. Congress of IAHR, Lausanne, Slritzerland, ppI77-I82.

Vale C and Sundby B (1987). Suspended sediment fluctuations in the Tagus estuary on semi-diurnal and fortnightly time scales. EsLuarine, coastal and shelf science, vol 25, pp 495-508.

West,rich B and Juraschek M (1985). Flow transport capacity for suspended sediment. 21sL IAHR Congress, Mel-bourne, Australia. pp 591-594.

White W R (1972). Sediment transport in channels: A general function. Hydraulics Research Station, Report No INT 104, pp21.

I,lilcock P R and Southard J B (1988). Experimental- study of incipient moti-on in mixed-size sediment. Water Resources Research, vol 24, No 7, pp1137-1151.

Zanke U (7977). Berechnung der Sinkgeschwindigkei-ten von Sedimenten, Mitt. des Franzius - Instituts fur WasserhauHeft 46, Seite 243, Technical University, Hanover.

Zhaohui W and Tiancheng S (1987). The effect of fine particles on vertical concentration distribution and transport rate of coarse particles. IAHR Congress, Lausanne, Switzerland, pp80-85.

Zhaoyin W (1987). Bouyancy force in solid-liquid mixtures. IAHR Congress, Lausanne, Switzerland, pp86-9 1.

20 APPENDIXI

Main workers in the field

(a) Internal

G V Miles (Tidal) NVModd (Tidal) R L Soulsby (Maritime) R Bettess (Rivers) P Lawrence (ODU) E Atkinson (ODU)

(b) Others

J Allard Laboratory Nationale d'Hydraulique. 6 quai Wati-er, 78400 Chatou, France.

J S Bridge Dept of Geological Science Univ of New York, Binghampton, New York,13901.

W R Brownlie W M Keck Laboratory of Hydraulics, California InsL of Technology, Pasadena, California.

R Deigaard (Denmark)

R J Garde Dept of Civil Engineering Univ of Roorbee, Roorbee U.P, India.

F M Holly Dept of Civil and Environmental Engineering, Univ of lowa, Iowa City, Ior^ra, USA. G J Klaassen Fluid Mechanics Group, Dept of Civil Engineering, Delft Univ of Technology, Delft, The Netherlands.

PA Ylantz Lamar Univ, Tescas formerly of Imperial College of Science and Technology.

RL Misri Dept of Civil Engineering, Regional Engineering College Srinagar, J and K, India.

G T Proffitt Ministry of Works and Development, Turangi, New Zealand.

G Ranga Raju Dept of Hydraulic Engineering Univ of Roorbee, Roorbee, U.P, India.

J S Ribberink Flui-d Mechanics Group, Dept of Civil Engineering, DeIft Univ of Technology, Delft, The Netherlands.

L C van Rijn Fluid Mechanics Group, Dept of Civil Engineering, Delft Univ of Technology, Delft, The Netherlands.

B R Samaga Dept of Civil Engineering Karantaka Regional Engineering College, Suratkal, Karanotaka.

S Sengupta Geological Studies Unit, Indian Statistical Institute, Calcutta, 7000 35, India. A J Sutherland Civil Engineering Department, Univ of Canterbury, Christchurch, Nelr Zealand.

APPENDIXII

Additional References

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Brownlie W R (1985). Compilation of alluvial channel data. ASCEJ of Hydraulic Engineering, vol 111, No 7, pp1115-1119.

Ho1ly F M and Karim M F (1986). Simulation of Missourj- river bed degradation. ASCEJ of Hydraulics Engineeri.ng, vol 112, No 6, pp497-5I7.

Hol1y F M (1986). Numerical simulation in alluvia1 hydraulics. 5th Congress of IAHR, Asian and Pacific Regional Division, Seou}, Korea, pp79-99.

Holtorff G (1983). Steady bed material transport in alluvial channels. ASCEJ of Hydraulic Engineering, vol 109, No 3, pp368-384.

Hydraulics Research Ltd. Report No SR 75 (1986). Numerical model simulation of entrainment of sand bed material 22pp.

Hydraulics Research Ltd. Report No SR 148 (i988). A numerical sand t.ransport model with time dependent bed exchange.

Hydraulics Research Stati-on (1973), Report No DE9. The Wash water storage scheme, numerical model studies of the Great Ouse estuary - a transport function for fine sand in the estuary. 35pp. Ikeda S and Asaeda T (1983). Sediment suspension with rippled bed. ASCEJ of Hydraulic Engineeri.ng, voI 109, No 3, pp409-423.

Klaassen G J (1987). Armoured river beds during floods. Euromec|r2I5, Genova, Ita1y, pp225-230.

Mantz P A (1983). Semi-empirical correlations for fine and coarse cohesionless sediment transport. Proc.'Instn Civi} Engineers, Part 2, vol- 75 No 3, pp1-3.

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Parker G (1987). Governing equations for longitudinal grain sj-ze varj-ation due to di-fferential sorting and abrasion in rivers. Euromech215, Genova, ftaly, pp2l7 -220 .

Ribberink J S (1987). Mathematical modelling of one-dimensi-onal-morphological changes in rivers with non-uni-form sediment. Communications on hydraulic and geotechnical engineering. Delft Univ. of Techonology, zuupp.

Ribberink J S and von der Sande J T M (1985). Aggradation in rivers due to over loading - analytical approaches. IAHR J of HydrauLic Research, vol 23, No 3 pp273-283. van Rijn (i981). The measurementof sediment concentrations in tidal conditions. 19th Congress of IAHR, Nev De1hi, Tndia, pp525-534. Shen H W and Hung C S (1983). Remodified Einstein procedure for sediment load. ASCEJ of Hydraulic Engineering, vo1 109, No 4, pp565-57B.

Shen H W and LU J Y (1983). Development and prediction of bed armouring. ASCEJ of Hydraulics Engineer, voI 109, No 4, pp61I-629. di Silvio G (1987). Adaptation processes through the surface of sedimentary systems. Euromech 215, Genova Italy.

Singh V P and Scarlatos P D (1985). Sediment transport on vertically two-dimensional_ man-made canaLs. 21st IAHR Congress, Melbourne, Australia, pp577-582.

Tanapore Z S (1981). Engineering applications of sediment theories to the fluvial and coastal environment. 19th IAHR Congress, Ner,rDelhi, India, pp86-133.

Todoravic P (1982). A stochasic model of longitudinal dispersion of bed sediment based on the granulation function. Advances in Water Resources, voI 5, pp42-46.

Walton T L and Douglass S L (1985). Stochastic sand transport using ARIMAmodelling. 21st IAHR Congress, Mel-bourne,Australia, pp166-I72.